Related papers: Non-linear Constrained Realizations of the Large S…
Computational reconstruction plays a vital role in computer vision and computational photography. Most of the conventional optimization and deep learning techniques explore local information for reconstruction. Recently, nonlocal low-rank…
We present a survey of the cosmological applications of the next generation of weak lensing surveys, paying special attention to the computational challenges presented by the number of galaxies, $N_{gal} ~$ 10$^{5}$. We focus on optimal…
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies…
We present a novel method for reconstructing weak lensing mass or convergence maps as a probe to study non-Gaussianities in the cosmic density field. While previous surveys have relied on a flat-sky approximation, the forthcoming stage IV…
Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can…
We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
The cosmic curvature density parameter has been constrained in the present work independent of any background cosmological model. The reconstruction is performed adopting the non-parametric Gaussian Processes (GP). The constraints on…
Observing system simulation experiments (OSSEs) have been widely used as a rigorous and cost-effective way to guide development of new observing systems, and to evaluate the performance of new data assimilation algorithms. Nature runs…
We propose a concealing-restoring system (CRS) for data on physical layer of the OSI reference model. CRS conceals those data by disturbing them with some random noises, and restores the data from the concealed ones to the original ones by…
The non-line-of-sight imaging technique aims to reconstruct targets from multiply reflected light. For most existing methods, dense points on the relay surface are raster scanned to obtain high-quality reconstructions, which requires a long…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
A fundamental drawback of kernel-based statistical models is their limited scalability to large data sets, which requires resorting to approximations. In this work, we focus on the popular Gaussian kernel and on techniques to linearize…
Fourier-based wavefront sensors, such as the Pyramid Wavefront Sensor (PWFS), are the current preference for high contrast imaging due to their high sensitivity. However, these wavefront sensors have intrinsic nonlinearities that constrain…
The real-world applications in signal processing generally involve estimating the system state or parameters in nonlinear, non-Gaussian dynamic systems. The estimation problem may get even more challenging when there are physical…
Mapping the underlying density field, including non-visible dark matter, using weak gravitational lensing measurements is now a standard tool in cosmology. Due to its importance to the science results of current and upcoming surveys, the…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
We address the generation of initial conditions (ICs) for GRAMSES, a code for nonlinear general relativistic (GR) $N$-body cosmological simulations recently introduced in Ref. [1]. GRAMSES adopts a constant mean curvature slicing with a…